Gradient expansion, curvature perturbations and magnetized plasmas

TL;DR

This paper develops a gradient expansion approach to describe pre-decoupling magnetized plasmas, linking relativistic inhomogeneities with plasma dynamics and curvature perturbations in the early universe.

Contribution

It introduces a novel gradient expansion framework for magnetized plasmas that relaxes previous small-inhomogeneity assumptions and connects with the separate Universe paradigm.

Findings

Derived two-fluid and magnetohydrodynamical equations with spatial gradients.

Presented solutions in anti-Newtonian and quasi-isotropic regimes.

Analyzed nonlinear evolution of magnetized curvature perturbations.

Abstract

The properties of magnetized plasmas are always investigated under the hypothesis that the relativistic inhomogeneities stemming from the fluid sources and from the geometry itself are sufficiently small to allow for a perturbative description prior to photon decoupling. The latter assumption is hereby relaxed and pre-decoupling plasmas are described within a suitable expansion where the inhomogeneities are treated to a given order in the spatial gradients. It is argued that the (general relativistic) gradient expansion shares the same features of the drift approximation, customarily employed in the description of cold plasmas, so that the two schemes are physically complementary in the large-scale limit and for the low-frequency branch of the spectrum of plasma modes. The two-fluid description, as well as the magnetohydrodynamical reduction, are derived and studied in the presence of the spatial gradients of the geometry. Various solutions of the coupled system of evolution equations in the anti-Newtonian regime and in the quasi-isotropic approximation are presented. The relation of this analysis to the so-called separate Universe paradigm is outlined. The evolution of the magnetized curvature perturbations in the nonlinear regime is addressed for the magnetized adiabatic mode in the plasma frame.